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\chapter{Discussion and Conclusion}\label{chap:Chp6}
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%\begin{abstracts}        %this creates the heading for the abstract page
%The chapter examines how the literature of social networks accounts for social transactions (i.e., acts of communication and interactions). Anchoring the dynamics of social networks in social transactions is coherent with a broader program to provide theories of social change with micro-foundations of social action. The chapter is divided into three sections:
%\end{abstracts}


%\begin{abstracts}
%This paper develops a method to analyse email communication networks in terms of the effectiveness of emails to elicit a reply. Four factors are considered: the email's sender (sender effect), the email's recipients (recipient effect), specific properties of each sender-recipient dyad (dyad effect), and specific properties of the email (stimulus effect). A multilevel model is developed and applied to an email communication dataset. The fitted model suggests that dyad and stimulus effects are more important sources of variability in reply rates than sender or recipient effects. Moreover, the correlation between sender and recipient effects is found positive when taken in isolation, but vanishes when  accounting for the dyadic effect. The strength of this method lies in the general and systematic way it provides to evaluate organization members and their ties with respect to their influence on others to reply. From a socio-theoretical perspective it operationalizes a co-evolution process that operates not only at the meso-level (nodes and dyads), but also between the meso-level and the micro-level (transactions).\end{abstracts}


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%   \caption[Hercules Killing Ant\ae us]{\textbf{Hercules Killing Ant\ae us}- by lifting him in the air, separating him from the Earth from which he gathers strength.}
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\begin{quotes}
Wandering through the frontiers of the sciences, and the arts, I have always trusted the eye while leaving aside the issues that elude it. It can mislead, of course, therefore I check endlessly and never rush to print.\\

\mbox{}\\
Meanwhile, for over fifty years, I have watched as some disciplines exhaust the `top down' problems they know how to tackle. So they wander around seeking totally new patterns in a dark and deep mess, where an unlit lamp is of little help. \\
\mbox{}\\
But the eye can continually be trained and, long ago, I have vowed to follow it, therefore work `from the bottom up.' Like the Ant\ae us of Greek myth, I gather strength and persist by often touching the earth. \\
\mbox{}\\
A few of the truths the eye told me have been dis-proven. Let it be. Others have been confirmed by enormous and fruitful effort, and then blossomed, one being the four thirds conjecture in Brownian motion. Many others remain, one being the MLC conjecture about the Mandelbrot set, in which I believe for no other reason than trust in the eye. \\
\attrib{{Benoit Mandelbrot, \\ Response to the Edge Annual Question} \citeyearpar{mandelbrot2005}   }
\end{quotes}

\clearpage
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\section{Introduction}

This work is driven by the following question: what are some of the mechanisms that link social transactions with network level entities: the individuals and ties that make it up, and the various structures that characterize it. The two empirical chapters demonstrate some of these mechanisms: Chapter 5 shows how the social action of replying to an email is influenced by entities at the micro-level (the email stimulus itself) and at the meso-level (properties of individuals involved in the transaction and the social tie that binds them.) Chapter 4 demonstrates how private and broadcast emails are stimuli (at the level of transactions) that prompt different types of responses (reply, reply-all or forward,) at the aggregate level contributing different types of structures to the network. 

This final chapter discusses these findings in greater detail and concludes the thesis. It begins with a general critique of the entire work and an attempt to address it, and then organizes the empirical findings  in light of the Coleman diagram (see section~\ref{sec:colemansboat},). This is  followed by a summary of the contributions, the limitations of this work and a critique of sorts. The chapter ends with a debate within the social sciences about the role and significance of digitally mediated transaction datasets. 

%Reacting to the abstract and introduction of this thesis, one reader wrote in a private email sent on  May 3\textsuperscript{rd} 2013: `I don't expect to be very enthusiastic about the dissertation. The introductory chapter gives me the impression that the data do not allow for a test of the theories because they contain information only on events, not on ties.' 
% Regarding the concern that the empirical chapters make use of data that refer only to transactions, not to ties. How then, could I make any claim about ties if I have no data about them? This is a valid concern, since the only empirical data offered in this dissertation is at the micro-level of email transactions. No independent data at the meso-level is considered, in contrast to the study published by \citet{quintane2011} for example, an innovative paper that demonstrates systematic differences between observed transactions and reported ties. 
\section{Learning about social ties from transactions alone}\label{sec:Chp6DeNooy}
The last empirical chapters have raised a general concern among readers of earlier drafts, a concern that  I would like to address upfront. The  problem arises from the gap between the concept of social ties and the type of data used in this dissertation. Throughout the dissertation a claim was made, that social ties cannot be simply reduced to a bunch of transactions (both in the introduction chapter and especially in section~\ref{sec:chp2TakingTransactionsSeriosly}.) In other words, I argued for a distinction in kind between ties and transactions.  However, the empirical chapters made use of data that refers to transactions exclusively, not to social ties. How then, could I make any reasonable claim about ties if I have no (independent) data about them? 

This is a valid concern, and the lack of independent data sources for social ties is indeed a limitation, compared, for example, to a study authored by \citet{quintane2011}. However, there are two ways of responding to this concern. 

\subsection{Ties and Transactions: a difference in order?}\label{Chp6:DifferenceInOrder}
First, many reject the distinction in kind between transactions and ties, insisting on defining the latter in terms of the former (see section \ref{sec:chp2Aggregation}.) That is one way to make the problem go away because if we define the network in terms of the patterns of transactions, all there is to know about ties is already in the transactions, simply by virtue of the definition we choose for the tie.\footnote{Perhaps it would be useful to use different terms, one for ties that are defined in terms of its transactions and one defined more broadly, a social tie that carries meaning to individuals, including mutual expectations, commitment, obligations etc. But since this is not a common practice in the literature, and in many cases claims and arguments are valid for ties of both sorts, I shall stick to the term `ties.'} Such a definition was used in Chapter 4, where two individuals were connected by a tie if one of them sent an email to the other. There is nothing outlandish about the claim that one can define the macro in terms of micro entities (definitional macro-micro link in section~\ref{sec:colemansboat}.) On the contrary, this claim is closely related to claims made by Max Weber, George Caspar Homans and \citet{monge2003} (as discussed in section~\ref{sec:chp2Aggregation}.)

Arguing that there is nothing interesting to say about ties just because the data is all about transactions, is equivalent to the argument that there is nothing interesting to say about networks if all you have is data about individuals and ties. Such a claim would pull the rug from under the feet of much of the body of network studies that rests on survey based, traditional network datasets, since these are nothing but reports of people's personal ties. It would be rather puzzling to claim that you cannot study networks just because you do not have an independent source of information on the network as a whole (such as an organigram in formal organizational settings, or by following the paradigm of Cognitive Social Structures \citep{krackhardt1987} for example.) But in practice, most empirical studies of networks do not rely on anything but a set of personal ties, those reported by individuals in surveys or interviews. Those are aggregated to form the network, without taking into account any independent measure at the (macro) level of the network. And although they have only data about ties, researchers can still say a whole lot about networks as a whole. 

Are networks anything different than a collection of individuals, their properties and the ties connecting them? Holists would argue that the answer is probably yes, whereas most nominalists would accuse holists of engaging in mysticism.\footnote{See Tarde's quote opening the Chapter 2.} There is little hope that this ontological question about the link between the whole and its parts will be solved any time soon. But I don't think we have to reach a resolution of this debate in order to recognize that whatever one's conviction on the matter is, those who treat networks as completely reducible to individuals and their connections still have interesting things to say about networks. By the same token, even if we accept that ties are something `over and above' transactions, those who define ties in terms of transactions might still have something interesting to say about ties.

How do transactions (sending an email for example) compare to network events (tie formation, dissolution etc. see section \ref{sec:Chp2MacroMeso})?  Some authors \citep*{denooy2011,brandes2009,butts2008} do not find anything very interesting in the analytical distinction between these two types of events, transaction-events at the micro level and network events at the meso-level of ties and nodes. For them, engaging in a social transaction involving two actors is a kind of `selection' mechanism, because a transaction consists of actors selecting with whom they interact, just like the formation of ties. For example, \citet{denooy2011} considers the act of publishing a review on a book equivalent to a `selection' event in which a new tie is formed between the critic and the reviewed author. \citet*{brandes2009} write that the only difference between surveying people about their social ties and collecting data about transactions (email, phone-calls etc.) is a technical one, namely that the former are 'panel data' and the latter 'event data.' The consequence is that event data includes the precise moment in which the event occured, and panel data only includes the information that it occurred at some unkown moment between two panel waves. But this is just a technical difference, one with implications on the statistical method and not one which is of any theoretical significance. The authors consider political events such as `visits, agreements, and provision of military aid, accusations, threats and military actions' as tokens of the type tie-formation. Most explicitly, \citep{butts2008} claims that 'relational events are temporally local phenomena, and thus represent the opposite end of the temporal continuum from the (relatively) long-term structures that have formed the primary subject matter of classical network analysis.'

Those authors do have a point: in some situations the distinction between network events at the meso-level of ties and transactions at the micro-level may seem redundant, indeed a hair-splitting exercise. They are also right to point out the similarities between events on both levels of abstraction. For one thing, note the principle of interdependency between events, one event triggering the next in sequence. Sending an email to two recipients makes it likely that the two will start contacting one another, an example of one social action triggering the next in a stimulus-response chain of transactions. By the same token, befriending two strangers makes it likely for these to become friendly one day. But whereas the first example is clearly a stimulus-response link between two transactions, would we be comfortable to say that the second example is of the same kind? 

\subsection{Ties and Transactions: a difference in kind?}
There is a second, stronger and perhaps more controversial \citep{vromen2010,abell2010} answer to the concern. We could maintain the claim that ties and transactions are different in kind, but qualify the claim by adding that they are not completely orthogonal to one another, both levels of analysis influencing, shaping and leaving their traces in one another (in other words, there exists a process of co-evolution.) Even for those who accept this argument, the problem goes away,  at least to some extent. By virtue of the mutual influences between ties and transactions, one could impute properties of the ties by observing transaction data alone, just as one could look at a person's traces in the sand and say something reasonable about the person's properties without actually having independent data about the person herself. Indeed, this is exactly the approach taken in Chapter 5. 
 
Having no direct or independent access to a phenomenon does not mean that we cannot gain knowledge of it. This is really the basic assumption of epistemic realism. In simple terms, consider the way latent variable analysis works. We accept the existence of a latent construct, say intelligence, a feature of an individual to which we have no direct access and no independent measure. It would not do to ask a person how intelligent she is, because she might not know. Instead of observing intelligence directly, we gain access to indicators of intelligence, so-called manifest variables measuring related properties such as mathematical and verbal performance. By measuring what is easy to access and making several reasonable assumptions about the distributions of a property in the population, we can say a whole lot about that which is unknown and not directly accessible to independent measurement. There would be few people who would claim that intelligence is defined by, or reducible to mathematical and verbal performance. And yet the consistent correlation between these skills suggests that there is some third confounding variable that drives the correlation between these two indicators. 

How does that relate to the link between transactions and ties? In the previous subsection I introduced an argument made by scholars who reject the distinction in kind between social transactions and ties. But there are counter-arguments as well, some of which were discussed in section \ref{sec:chp2TakingTransactionsSeriosly}. It seems to me that the arguments for a difference in kind between transactions and ties are more convincing, but my point is that whether one agrees or not, transaction data is a sufficient resource to learn about processes of co-evolution between transactions and social ties, independenly of how one might define the latter.


%. Granted the similarities between network events and transactions, networks abstract away details about the process and context in which ties are `activated,' completely innocent of the possibility that every transaction can span multiple actors and ties, and every tie can be associated with multiple transactions as \cite{Feld1981} rightly notes. As far as the network model is concerned, all that matters is that ties have been formed. And the kind of exercise they are interested in is whether tightly knit groups come together because they are similar in character (homophily/selection) or because of a general tendency in the network towards transitivity \citep{wimmer2010}. 

%The micro-level details about sequences of transaction events that yielded the ties are abstracted away to form the network model, specifically details as to whether ties were activated within a single social transaction that spans distinct ties concurrently or whether multiple `situations' were involved, each  associated with one tie. But these details are important, as the previous chapter and this one illustrate; micro-level details have important consequences for the formation of new ties at a higher level of aggregation.  

\section{The empirical findings in light of micro-foundations}

Recall that the research question asked us to identify mechanisms of co-evolution between communication transactions and network structures in the context of email communication. In more detail, we would like to know how we might use (email) transaction data to account for the links between the macro-level of the group, the meso-level of social ties (properties such as strength etc.)  and the micro-level of social transactions (sending an email, replying to one etc.) Special attention was given to the distinctive properties of emails as a communication medium, specifically the notion that emails have the property of being assigned to multiple recipients. We shall now review the findings and try to fit them into the Coleman diagram depicted in figure~\ref{ImgColemanContributions}.\footnote{A note of caution: the diagram is a loose and general framework. It works well for diffusion processes as discussed in section~\ref{sec:colemansboat} and I suppose it was built with this kind of process in mind, but it is applicable in many other organizational contexts as well \citep{abell2010}. But I think there are cases where the assignment of explanation to an arrow in the diagram could be somewhat loose. } 


\subsection{Chapter 5 Results and micro-foundations}
Let us start with the findings in Chapter 5. An incoming email (stimulus) lands in the inbox of one of its recipients, and the recipient has to make a decision between two courses of action: to reply or not to reply. The situation is similar to the one facing the doctor in Coleman's hospital, as she faces the decision whether to adopt the new medicine or not \citep{coleman1957}. We must imagine the recipient (or the doctor) at the lower right hand of the Coleman diagram, two types of `forces' or considerations impinging on her. Arrow number $2$ in the diagram represents the unique properties of the transaction preceding the moment of decision and influencing its outcome. In the recipient's case it was the stimulus email, in the doctor's case it was the consoltations she had with colleagues.  

\figuremacroW{ImgColemanContributions}{Organizing the contributions according to Coleman's diagram.}{Main contribution of Chapter 5 along arrow number $2$ and $2a$, main contributions of Chapter 4 along arrow number $3$}{.60}

The results in table~\ref{tbl:Chp5Results} indicate significant effects that include but are not limited to the number of co-recipients and whether or not the recipient was assigned to the \textit{\textbf{to}} field on the message. Confirming the findings from Chapter 4, we find that the more recipients associated with the email, the less likely the reply. In contrast to the findings from Chapter 4, here we have direct evidence that the relation between the incoming transaction and the outgoing one is of a stimulus-response type, and not independent messages flowing both ways. In addition, we find that the assignment to the \textit{to} field increases the chances of a reply - both effects are significant. In addition, there is a significant effect of variability that is due to the message itself. That is, variation in reply-likelihood between the decisions made by recipients of the same message is significantly less than the overall variation in reply-likelihood. There are some unknown factors unique to the message itself that affect the rate of reply, most probably due to its content or the moment in which it was sent. Something specific in the message and not the identity of the sender nor the receiver nor the combination of the two is responsible for this, since those were  controlled for.

Besides the effect of the message, there are effects of the identity of the sender, the recipient and the tie between them. These are captured by arrows number $1$ and number $2a$. Both arrows reflect the effects that macro/meso conditions have on the decision of the recipient, and they include the organizational roles of the sender and the recipient, their individual properties that might influence them to deviate from the average likelihood to reply, and the properties of the relationship between them. 

Of all these, the most relevant for the debate about the nature of the social tie, is the variation in the likelihood of reply that is associated with the specific sender-recipient dyad, after controlling for the overall properties of the sender and the recipient. First, on the dyad level, the frequency of email exchange prior to the email in question is not significant, after controlling for the other variables. This is rather surprising, because it means that the likelihood to reply is not significantly correlated with the frequency of messages exchanged after controlling for the other factors.\footnote{Recall that from Granovetter's definition of the strength of ties \cite{granovetter1973}, frequency of exchange and reciprocity are both associated with the strength of the tie, so we might expect a correlation here. In this context the lack of correlation between reciprocity and exchange rate was also found in mobile data by \cite{kovanen2010}.}

But I think that conceptually, the most interesting finding is the significant variability that is attributed to the dyad, after controlling for all other issues. What is at stake here is that between two individuals $A \text{ and } B$, $A$ could have a lousy sender effect (virtually nobody replies to her emails) and $B$ could have a lousy recipient effect (virtually never replying to her emails.) However, when $A \text{ sends } B$ a message, the rate of reply is exceptionally high. There is something latent in the dyad, the relationship between the two actors that influences the likelihood for reply, in a manner that cannot be explained by looking at the overall properties of the two individuals separately. 

This can be seen as a novel method to measure a property of the tie, a method that does not depend on the frequency of exchanges. It is the property of the dyad that influences the likelihood of replying to an email, and there is substantial variation between one dyad and another in respect to this value. This attribute is closely related to Granovetter's definition of strength of ties \citep{granovetter1973}, when he defines it as 'reciprocal services.' 

Although the empirical investigation models a micro-level outcome, figure~\ref{modl1sender_recip} describes a pattern at the macro-level of the group as a whole, a slight but significant correlation between people's sender effects and recipient effects. The positive correlation suggests that in this group of people, those who have a higher (lower) than average sender effect also have a higher (lower) than average recipient effects. Those who tend to receive more (less) replies to their emails tend to reply more (less) freqeuntly. Putting it a bit extravagantly, in this group, one might conclude, there is an overall sense of justice when it comes to replying to emails. This macro-level pattern is a result of the aggregation of many patterns of reply at the micro-level, and is therefore associated with arrow number $3$ in the Coleman diagram. 

\subsection{Chapter 4 Results and micro-foundations}

Let us now turn to the results from Chapter 4. The key result is that private emails contribute more to the reciprocity of the network and less to its transitivity, as compared with broadcast emails. We do not have any hard evidence to suggest why this is the case, but there are some reasonable explanations for this, all of which have to do with the way people use the email medium to carry out their communicative transactions.  Thus, these results are associated with arrow number $3$ in the Coleman diagram, micro-level transactions give rise to network level patterns. I shall now suggest several explanations that could explain why we might see diminishing reciprocity\footnote{Note that I use here `reciprocity' to denote stimulus-response type patterns, where the incoming email is the stimulus and the response of the recipient is in the form of a reply. Reciprocity thus defined has not been tested directly in Chapter 4. What was measured was merely two-way communication exchanges between pairs of actors, or symmetry. To test stimulus-response transactions in the data, it would be necessary to identify and associate between stimulus messages and response messages, for example by comparing between subject line fields, as was done in Chapter 5. } with increasing recipient number. 

\begin{enumerate}
\item The simplest explanation is that this is a spurious correlation and there is a third confounding variable which affects both reciprocity and recipient number. The confounding variable is the reason (read: purpose, motivation, expectation) of the sender for sending the stimulus email. When individuals make an announcement or want to disseminate information, they may want to act on a large group of people and make them  aware of the content of the message without necessarily expecting them to act upon it. To achieve their purpose, senders dispatch emails to a large group of individuals (hence `broadcast message',) signaling to recipients that a reply is not expected. According to this mechanism, recipients do not refrain from replying because of the long recipient list per-se, but because they judge that the sender does not expect them to reply. Hence the correlation between recipient number and reciprocity is confounded by the reason (expectations, purpose) for sending the email. In terms of the Coleman diagram, the decision of the recipient not to reply is the consequence of the transaction, therefore this mechanism is associated with arrow number $2$.

\item  Composing a single-recipient email involves a certain amount of time, attention, effort and resources, all concentrated on the relationship with a single contact. In contrast, when sending broadcast emails, the effort is distributed among its numerous recipients. From a theoretical point of view, one could apply exchange theory \citep{emerson1976} to explain why an incoming private email (especially a long one) might elicit a sense of obligation and duty to reply back, more so than an incoming broadcast email. Consequently, an act of reply to a private email would be driven either from the need to conform to a norm  (arrow number $2a$,) or from a strategic decision (arrow number $2$,) to pay off one's `social debt' to the sender. 


\item A related explanation would be that because of the greater effort per recipient inolved in private emails, sending them may be associated with a stronger tie. Recall that  \citet{granovetter1973} defines the strength of a tie in terms of `reciprocal services' and the `amount of time' associated with the tie. In this latter explanation, the strength of the tie operates as a confounding variable that drives both higher reciprocity and fewer recipients. Since the strength of the tie is a meso level property acting on both sender and recipients from the height of the meso-level, it would act on the sender via arrow $1$ (driving her to send private emails to her strongest contacts) and on the recipient via arrow $2a$, driving her to reply to her strongest contacts by virtue of the strength of the tie connecting them. 

\item Another mechanism could be related to the theory of collective responsibility or social loafing \cite{Karau1993}. According to this argument, the `responsibility' to reply is `distributed' among the recipients. As their number increases, a higher level of `defection' (read: no reply) is expected. Here the recipient is acting strategically along arrow $2$, her decision interacting with what she hopes would be the decision of other co-recipients. 

\item  Finally, consider a mechanism that operates in the opposite direction to those mentioned above. The success of spam (unsolicited bulk email) to elicit a response among recipients relys on being distributed to numerous recipents \citep{cranor1998}. The more recipients, the more likely to elicit a response. This is an interesting exception to the mechanisms mentioned above  because flooding the system with emails is a macro-to-micro process acting on individuals through arrow number $2a$. Arguably, the act of sending unsolicited mail is no longer at the micro-level of transactions but at the top left corner of the Coleman diagram, impinging on a large collective. Notice the difficulty to adjudicate whether a social-phenomenon (such as sending out broadcast emails,) should be taken at the micro-level or the macro-level. I suspect this marks the beginning of the cracks in Coleman's theoretical framework, an issue I shall return to in section~\ref{sec:Chp6Coleman}. 
\end{enumerate}

\noindent Of course these  mechanisms should mark the beginning, not the end, of an entire empirical investigation, one that attempts to tease out which if any of these mechanisms operates, what are their relative strengths in driving a reply to an email, under what conditions and in what contexts does each of them operate. 

The second important finding in chapter 4 suggests that broadcast emails contribute to the transitivity of the network. This means that they tend to be sent to people who exchange email messages. There could be one of two explanations for this; either the broadcast emails acts as a stimulus, triggering direct exchange among co-recipients (micro-micro link associated with arrow number $2$,) or the email was sent to these recipients together because the sender knows they are already connected to one another (macro-micro link associated with arrow $1 \text{ or }2a$). It is also possible that multiple recipient emails are part of discussion threads among a group of people, and the discussions proceeds every time one of the recipients uses the `group-reply' feature, thus increasing transitivity in the network. For example, given a broadcast email sent to $n$ recipients, the first to use the `group-reply' feature adds $n-1$ triangles to the network, possibly increasing transitivity in her region substantially. The transitivity finding is related to two additional empirical results. 

\begin{enumerate}
\item There is a distinction between sending one broadcast email and sending multiple private emails, the former being a better indicator of contact between  recipients than the latter. But this type of distinction is meaningless when we look for the equivalent at the meso-level of social ties. Transitivity at this level only tells us that when strangers share a common friend, they are likely to become friendly themselves. When applied to the macro-level of tie configuration, transitivity is more abstract and simple. Taken down to the micro-level of transactions, we need to be more precise about the properties of the transactions taking place. 
\item Another interesting result is seen in figure~\ref{ImgRecipCluster}. As the number of email recipients increases, and against the background of steadily declining reciprocity,  the level of transitivity first increases, reaches a maximum and then begins to decrease. If the assumption is true, that transitivity levels reflect group discussions, perhaps the peak of the curve designates a socially significant value, such as an optimal number of participants for collaboration or discussions in emails. However, at this point we cannot be sure. To further explore this proposition one needs to study the chains of related messages.
\end{enumerate}

\noindent Taking both findings together, the recipient number correlated with reciprocity and transitivity, we reach a rather surprising conclusion which I will explain below. The conclusion is this: if we adopt the definition of the strength of ties from \citet{granovetter1973}, we see a violation of the strength of weak ties hypothesis  in the context of email mediated transactions. Though it would be hasty to claim that this is a general law, the explanations I offered above, to the extent that they are the ones that account for the observed pattern, are not context dependent. They suggest that the violation has something to do with the way people communciate with one another through the medium of emails in general. 

Let me explain where the violation comes from. Recall that the hypothesis states that stronger ties are embedded in network regions of higher density. But this cannot work in the context of emails if we accept the key finding that private emails contribute more to the reciprocity of the network and less to its transitivity, as compared with broadcast emails. On the contrary, private emails are associated with more reciprocity and more frequent exchanges. %\footnote{Private emails are much more common than broadcast emails, the distribution of emails declines with recipient number as shown in figure~\ref{ImgRecipMessage}. This is a common finding, reported also by \citet{quintane2011}.} 
Thus, private emails are consistent with the stronger ties. However, group level discussions and collaboration tasks require broadcast emails, which also contribute more to transitivity, and the `reply-all' feature increases the number of closed triangles substantially, even if only a few of the recipients use it. Thus it is the stronger ties that are mediated by private messages, which are not embedded in dense regions. Weaker ties that are mediated by broadcast messages are embedded in denser regions. As long as these two mechanisms are at work, they push the network to violate the strength of weak tie hypothesis. %\footnote{Add to that the attempt to verify the hypothesis, an attempt that failed to reach significance.}

This is probably the most interesting finding in the Chapter, a mechanism associated with arrow number $3$ in Coleman's diagram: under certain conditions and thanks to the unique features of the email artefact, email communication networks violate Granovetter's strength of weak ties hypothesis. 




\section{Review of the contributions and critique of sorts}
This section consists of a brief overview of the main contributions of the thesis, organized into three categories as follows. 

\subsection{Distinctive Properties of Networks of Transactions}\label{sec:Chp6Distinctive}
\begin{quotes}
Insanity in individuals is something rare - but in groups, parties, nations and epochs, it is the rule\\
\attrib{Friedrich Nietzsche, Beyond Good and Evil}
\end{quotes}

\noindent The micro-macro distinction is a fundamental theoretical foundation, well known both in the social and physical sciences, even marking an institutionalized division of intellectual labour between microeconomics and macroeconomics. Whereas micro-economics addresses individual entities (such as buyers, sellers, households, firms) as they behave within an exogenously given environment,  macroeconomics addresses the aggregate effects of economic activity (such as inflation, unemployment, productivity.) These and other intellectual projects demonstrate time and again, that even if we define the collective in terms of individuals and nothing `over and above,' we find system effects. By this I refer to phenomena in which the properties of the aggregate differ from the properties of its members  taken one by one. Here are some examples of famous system effects: 
\begin{enumerate}
\item \textit{\textbf{Condorcet's Paradox.}} Transitivity does not scale, so that even if each individual in a group has transitive preferences, aggregate preferences of the group are intransitive \citep{gehrlein1983} .
\item \textit{\textbf{The Doctrinal Paradox.}}  Logical consistency does not scale, so that even if each  individual in a group is logically consistent, aggregate judgement of the group is logically inconsistent \citep{list2002}.
\item \textit{\textbf{The Prisoner's Dilemma.}} Utilitarianism does not scale, so that even if each individual in a group is rational and utilitarian, their decisions interact with each other making all concerned worse off. 
\end{enumerate}

\noindent The above examples are taken from economics, game theory and political science, and there are plenty of additional examples from physics \citep{Anderson1972}, law \cite{Vermeuele2009} philosophy and sociology \citep{elster1989b,jervis1997}. It would be incorrect to say that this dissertation addresses system effects, but perhaps one could say that it handles a problem that has a weak form of family resemblance with these effects. I mean this in the sense that theories and concepts that work at the level of traditional social networks, seem to work differently at the level of networks of email transactions. 

Obviously, such differences are known in the literature and some have been reviewed in previous chapters. Recall, for example, the study by \citet{quintane2011}, comparing between two social network models associated with the same group of $23$ individuals, one model based on reported ties and the other based on email mediated transaction data. The study finds different network mechanisms operating in the two network models.  \citet{kovanen2010} find a complicated relation between the reciprocity of calls, and their frequency and duration in the context of mobile phone communication networks, which is not what one expects to find in social networks. Finally, \citet{liben2008} find that chain-mail networks exhibit very different properties from the small-world network of email users that produced it. All these studies indicate that when considering the `nuts and bolts' of digitally mediated transactions, aggregate patterns have very different patterns to what one might expect from traditional network studies. This dissertation contributes to this line of thinking in a couple of ways. 
\begin{enumerate}
	\item \textit{\textbf{Mechanisms.}} Mechanisms operate in a different manner in traditional networks of friendship, say, and email transaction networks. For example, although the strength of weak ties has been confirmed in numerous studies of traditional social networks, in this thesis I argued why there might be a mechanism that operates in the opposite direction in the context of email networks. Here is a mechanism that works one way at the level of social ties, and another at the level of email-transactions. There might well be other such mechanisms.
	 
	\item \textit{\textbf{Concepts.}} Various well known concepts from traditional network literature seem to work differently in the context of email mediated transactions. Traditional network literature takes notions such as reciprocity and transitivity, abstracting them away from the medium of communication and interaction in which they are preformed \citep[this critiqe very similar to the one raised in][]{feld1981, feld1982a}. More specifically, it is completely innocent of stimulus-response chains that are the defining property of human transactions \citep{gibson2005}. This innocence is not due to oversight but is intended, part of the Durkheimian strategy inspired by the founding fathers of the field (see section~\ref{sec:Chp2Durkheimian}.) But chains of transactions have macro-level consequences. It is what drives the autocorrolation and burstiness of human transactions \citep{barabasi2005}, and it is what  drives reciprocity in Chapter 5 and most probably in Chapter 4 as well. Let us consider a couple of typical network concepts in this light.
	\begin{enumerate}
	        \item \textit{\textbf{Reciprocity.}} In traditional network research, the term simply denotes matter, services or information flowing between two individuals in both directions. At the level of transactions it means that what flows in one direction is linked to what flows in the other via a stimulus-response process. Reciprocity at the micro-level is thus understood as a stronger version (or narrower definition) of reciprocity at the macro-level.
	        \item \textit{\textbf{Transitivity.}}  The abstract and general mechanism associated with the term in the context of traditional networks (strangers with common friends tend to become friendly) is qualified at the level of transactions. In the context of emails we need to make a distinction between, say, sending multiple private emails or sending one broadcast email, two transactions that have different consequences in terms of the likelihood of a mutual contact to induce a connection between strangers. 
	        \item \textit{\textbf{Degree Distribution.}} In traditional networks this term denotes the distribution of the number of friends. One could distinguish between in-degrees (number of nominations recieved in a survey method) and out-degree (number of nominations given.) But that's about it. The non-random distribution of degrees has attracted debate that spanned many decades \citep{moreno1938,barabasi1999}, partly because it is precisely the non-random distribution that is believed to conceal a peculiarly `social' mechanism. However, when we start looking at transactions, we see many more non-random distributions, each demanding a social explanation. Chapter 4 introduces three such distributions, the production, consumption and dissemination of emails, each of the distributions non-random for reasons that may be of some consequence.
	\end{enumerate}
	
	\item \textit{\textbf{Interdependencies.}} Over fifty years ago, Siegfried F.  \citet[p 227]{nadel2007} described  what he found most interesting in the concept of `networks' with the following visionary words: `\ldots I do not merely wish to indicate the `links' between persons; this is adequately done by the word relationship. Rather, I wish to indicate the further linkage of the links themselves and the important consequence that, what happens so-to-speak between one pair of [nodes], must affect what happens between other, adjacent ones.'  Nadel was looking mechanisms that govern tie-interdependency. In traditional networks, tie interdependeny works mainly through mechanisms such as popularity, transitivity and homophily. But in email transactions the logic is much more complicated, and it is noted not only by the observing scientist but also by the actors themselves. Multiple recipient emails are a powerful example of how connections between people are instantiated or reinforced in tandem. Recipients become aware of others' communicative transactions and study them in  detail, informing themselves of the existence of other co-recipients, looking at whether or not they were assigned to the \textit{to} field, assembling the evidence to judge the expectations of email sender and co-recipients, finally reaching a decision about the most adequate response. The type of interdependency at the level of transactions involve intention, purpose and meaning for the individuals themselves. At the level of traditional networks, they are much less concrete and immediate. 
	  
	\item \textit{\textbf{The technological medium.}} The medium through which people communicate is all but irrelevant for traditional work on social networks.\footnote{But see one exception in \cite{Licoppe2005}.} But the emphasis on transactions bring the distinctive properties of the technology into relief. Emails can be sent to a single recipient or to multiple ones. Recipients can be assigned to the \textit{to} field or to the \textit{cc} field. These are all small choices on the part of the sender, with consequences on the action of recipients. Unlike traditional networks where we find individuals connected to one another, here one person interacts with others via a medium, and the properties of the medium are involved in the transaction and influence its outcome. Furthermore, investigating transactions challenges the notion that technology is merely a great tool for researchers to elicit data  \citep{lazer2009}, and encourages the notion that it is an active participant in the situation, steering the network's unfolding structures.
\end{enumerate}





%Three mechanisms of tie-interdependency are referred to very frequently in the literature of social networks, namely \textit{popularity effects}, \textit{homophily} and \textit{triadic closure}\g \citep{snijders2006}. Despite the common reference to these effects in the literature, many are still worried with the `inadequacy' \citep{snijders2006,newman2003} of these mechanisms, partly because they are still not well understood in terms of the situational processes that give rise to, and sustain them. It is infrequent that people `decide' to establish new relationships or dissolve old ones, since changes in the status of ties are themselves the culmination of a process involving various situations, decisions, emotions, circumstances and mutual social transactions \citep{Lazarsfeld1954,hartup1997}. For example, the literature on friendship   \citep{hartup1997} makes an important distinction between deep-structure (based on reciprocity)  and surface structure (social exchange), and the mutual influences between these two levels of aggregation is precisely the theoretical motivation that guides the rest of the chapter. 

\noindent The first contribution is the distinction between networks of transactions and traditional networks of ties: different mechanisms are at work, and some of the concepts might need to be revised or qualified in order to capture more precisely the structures of transaction chains. Finally, the notion of interdependency becomes more qualified and the specific properties of the technological artifact play a more important role. 

\subsection{Methods and Limitations}
The methodological chapter (Chapter 3) problematizes the process of constructing network models from transaction data, highlighting information that exists in the dataset but through the process of its construction, disappears from the network model. It argues that this information is relevant for the exploration of social mechanisms that are involved in shaping the network. One example of lost information is the differences between private and broadcast emails. Two methods were developed in Chapters 4 and Chapter 5, that seek to address this issue to some extent.

The literature demonstrates that decisions made by modellers (e.g., thresholds, noise filtering techniques)  have an impact on the properties of the resulting network \citep{DeChoudhury2010,grannis2010}, but it is not clear what are the structural implications, say, of filtering out broadcast messages. For example, \citet{kossinets2006} filter out emails with more than four recipients. The findings in Chapter 4 suggest that filtering out broadcast emails would potentially underestimate transitivity and overestimate reciprocity in the network. 

The Chapter also developed a method to incorporate the number of email recipients into the strength of the tie, in a similar way carried out by \citet{newman2001a} for networks of authors of academic papers. Regression analysis  confirmed the hypothesized correlation between levels of reciprocity and the strength of the tie thus calculated. In Chapter 5, a different measure of a tie was devised, a value that indicates the likelihood that either of the individuals associated with the tie would reply to an email, controlling for their overall reply pattern and for the properties of the message. Both these methods could be used in future research for constructing networks. 

In addition, Chapter 5 devised a statistical method to tease out the various factors that  influence a recipients' decision to reply to an incoming message, and to compare between the relative importance of each factor. This method may have some practical applications. For example when launching marketing campaigns, companies may like to know why some campaigns are successful and others fail, what factors are involved in determining success/failure, and what is the relative importance of those factors. Factors to consider include the identity of the company launching the campaign (sender,) the identity of the customer (recipient,) the campaign itself (message) Or the special organizational relationships between a company and a customer (tie.) The method developed in Chapter 5 could suggest where to start looking for answers to these questions. 

There are several limitations to this work, and because of its exploratory nature it may raise quite a few questions and opportunities for further research. Some of the arguments could be presented more formally, so they could be more amenable to further study and investigation.  Theoretically, the previous sections introduced a whole range of mechanisms that could potentially explain the phenomena of reciprocity and transitivity in email network datasets. These could be rigourosly tested in order to understand how they work and how they interact. Most importantly in the context of Chapter 4, these  mechanisms all assume that observed structures of reciprocity and transitivity are due to stimulus-response type patterns at the micro-level of transactions. This assumption was only assumed, and it should be directly measured to verify that these are indeed the mechanisms at work. 

Empirically there is a potential to expand on the current work. first, there is a need to reproduce the findings in a different email datasets, ideally backed up with survey based network data. Additional datasets can rule out the explanation that the findings are unique to this set of empirical data. That said, I think the explanations are compelling and that the number of recipients is indeed a confounding variable that leads to a (spurious) negative correlation between reciprocity and transitivity. If such a violation is not captured in other datasets, one may want to investigate whether there is a different mechanism that works in the opposite direction. In that case there would be a need to control for that mechanism in order to disentangle the two. 

It may also be interesting to look for independent ways to confirm the violation of the strength of weak ties hypothesis. In fact, one attempt is made in Chapter 4 by regressing the strength of each tie against the ratio of mutual contacts of the two individuals associated with it. Unfortunately, no significance was found so it is hard to interpret the result, except saying that if the effect is there, this method of regression is either not adequate or does not have the power to capture it. In addition, a more systematic way is needed to compare between private and broadcast email mediated transaction networks, controlling  for issues such as network density. A natural candidate for such a method would be  ERGM,\g but the limitation with ERGM is that large data models often degenerate,\citep{snijders2006} and the method requires a rather steep learning curve to run it and interpret its results. In fact, not only does it fail to converge with large datasets, the assumptions that justify using it are incorrect when using it on large networks.\citep{snijders2006} In any case, it would be reassuring to find an independent way to confirm the violation of the hypothesis, both on another dataset and by finding an independent method to test the correlation between strength and local clustering. 

Also in Chapter 5 it would also be interesting to reproduce the findings in another dataset and consider adding more covariates into the model. These might include properties of individuals (their position in the organizational hierarchy for example) or even attributes of the tie such as reporting relations in organizational settings. In case there is independent survey data, one could add a covariate to flag whether or not a dyad was reported as a tie in the survey data. These covariates should control for some of the variation associated with the nodes and ties, as well as controlling for standard network mechanisms such as homophily. One could also consider grouping the emails according to their content and adding dummy variables to see if they control for the variation attributed by the emails, or better still, one could even group the emails into stimulus-response chains, and take the emails to be nested within the chains. One drawback of the model is that it is very complicated, consisting of crossed factors, multiple roles and a binary outcome variable. All this makes convergence difficult to attain in larger datasets, putting a limitation on the utility of this method.

Recall that the findings in Chapter 4 explained network patterns of reciprocity and transitivity based on stimulus-response type chains. But these chains were only assumed, not directly observed. The objective of Chapter 5 was to measure these chains directly, but work has been limited only to the mechanism of reciprocity. It would be interesting to complement this work with a measure of stimulus-response chains that account for transitivity. A question to investigate would be this: what is the likelihood for incoming broadcast emails to trigger email exchange between co-recipients? Though applied to transitivity, the objective here is the same, to link the network topological structures to sequences of stimulus-response type chains.


% limtiations: need to check the stimulus response type pattern in four, esp. transitivity, is it sent to people who are already connected or does it prompt connection. see how useful the strength of ties in 4,5 is, for example through DeChoudry etc...  try other email datastets, take a different medium or a similar one, such as chat groups or closed facebook groups that also circumscribe small groups.
%     
% % 	really hard to get things to converge. 


\subsection{The Coleman Diagram}\label{sec:Chp6Coleman}

From a theoretical point of view, this dissertation can be seen as an attempt to apply the Coleman diagram to the a study of email mediated networks, and now we are more or less in a position to judge how fruitful this attempt has been. I think that as a general theoretical, or rather meta-theoretical framework, the diagram has merits in guiding the process of investigation and aiding the interpretation of the results. It organizes the findings, mitigating the danger of macro-to-macro explanations and acting as a sensitization device to the role of micro-level transactions as a locus of structural change. It helps thinking about the necessity to tease out the effects into those that operate via micro-level transactions (arrow number $2$) and those that operate uniformly on all individuals via macro-level entities (arrows number $1$ and $2a$.)  Furthermore, it creates a common vocabulary for communicating and thinking about the findings and the way they complement one other. Associating the mechanisms with the various arrows produces a sense of completeness, ensuring a more or less exhaustive account of all the types of mechanisms involved in the process of change, lending the exploration a sense of progress in which one assembles different pieces of a puzzle into one theoretical whole. %For example, after coming across the correlation between recipient number and network structure, I associated this process with mechanisms that go from micro to macro in the diagram. This prompted me to begin thinking of how to operationalize 

Theoretically, the Coleman diagram facilitates the discussion of several  ideas. The lower part of the diagram is often said to be associated with the micro-level of interactions. This raises the question, should network events be considered equivalent to social transactions? The literature on the formation of friendship asserts that friendship is formed as a culmination of a process that involves multiple transactions \citep{hartup1997,Lazarsfeld1954}. This suggests that to reach rock-bottom explanations, one would need to dig deeper into transactions. 

The Coleman diagram does present challenges, though. For one thing, at times it is not clear whether the mechanism operating is arrow number $1$ or arrow number $2a$. A more serious issue is the difficulty in classifying entities. Take an email transaction for example. Transactions are invariably classified at the micro-level of analysis. But it is not clear whether one should classify a broadcast email at the group level (macro-entity) or at the level of transaction (micro-entity.) Furthermore, when a broadcast email is sent, it is associated with several ties. But ties are at a higher level of analysis, so what does it mean to say that a micro-level entity (email) is associated with multiple meso-level entities (ties?) Is this like saying that individuals (micro-level) are influenced by multiple norms (macro-level)? I think that the best way to use the diagram is to consider it as a general guide for the principles of micro-foundations, rather than to stick to every arrow religiously.
\subsubsection*{A modest proposal}
In one of the closing scenes of the film Barton Fink by the Coen Brothers, Charlie, a murderer who feigns to be a door-to-door insurance salesmen (`you might say I sell peace of mind,') gives a rectangular parcel to Barton Fink, a scriptwriter struggling with a writer's block. We never find out for certain what is in the parcel, but there are indications that it contains the severed head of one of Charlie's victims. Upon giving Barton the parcel, Charlie mutters: `Funny, huh, when everything that's important to a guy, everything he wants to keep from a lifetime - when he can fit it into a little box like that. I guess \ldots I guess it's kind of pathetic.'

Charlie ponders for a moment over the micro-macro mystery. He is holding a box that contains a head of an individual with a vast array of identities, experiences, memories, thoughts and emotions, a product of an entire lifetime, numerous contexts and situations which have all left their marks in an object that fits into a surprisingly small parcel. This individual is what Dennis H \citet{wrong1961} calls `the socialized man.' If Wrong is right saying that the individual is in some sense the product of so many macro-entities, it is almost tempting to allow the socialized man to enter Coleman's framework in the upper left corner, where macro entities dwell. But that corner is reserved for anything macro except individuals. All individuals belong to the micro-level, at the bottom of the diagram. 

This raises a puzzle: beyond being able to fit his severed head into a small parcel, in what sense is the `socialized man' a micro entity? How is he different from other macro entities, such as the price of a product at equilibrium, norms or institutions? There is no question that these two types of entities (individuals and the prices at equilibrium) influence one another, but in what sense is one micro and the other macro? Human interaction and transactions are typically considered to be micro events. Is the action of sending an email to multiple recipients a micro affair or a macro one? Some types of emails, unsolicited spam messages for example, are sent to thousands, perhaps hundreds of thousands of people - are these micro or macro entities?  Where exactly do they fit in the Coleman diagram? 

Stated more generally, what do we actually mean when we use the terms micro and macro? There's an intuitive answer, that the macro is large and the micro is small. But when conjuring different micro and macro entities, many of them are abstract and their size is not one of their properties, let alone a feature that distinguishes between them. Another answer is that every macro entity is associated with multiple micro entities. That is of course true, but the reverse is also true - every micro entity is associated with multiple macro entities. Think of the relationships between any two entities in the empirical chapters, they all seem to be of a many-to-many type: every individual is associated with multiple ties and vice versa, every email is associated with multiple individuals and vice versa, every tie is associated with multiple emails and vice versa. 

Even the relationship between networks and individuals is of a many-to-many character. Obviously, every network is associated with multiple individuals, but the reverse is also true. A single email network can be mapped into different sub-networks of activity, private emails and broadcast emails produce networks with strikingly different structural properties, both  existing in parallel on top of the same group of people. This image is analogous to the distinction between anatomic and functional networks known\citep{shalizi2006} from the study of neural networks, where one anatomic network of neuron-fibers can be mapped into multiple task-related functional networks (see the discussion in section~\ref{sec:FuncAndAnatomicalNetworks}). The same individual could be central in one such functional-network and marginal in the other, so the relation between individuals and networks is many-to-many and not one-to-many.



%every individual has many ties, and every tie has two individuals, which is micro and which is macro? Every mail is associated with multiple individuals and each individual with multiple emails, which is micro and which is macro? Even at the level of the network we have seen that individuals participate in various networks with completely different properties, sexual networks, friendship networks, organizational networks. Moreover, each anatomical network can be mapped to multiple task-specific or functional networks. Collaboration networks which are mediated by broadcast emails have a completely different form than networks which are mediated by private emails, two types of networks that vary in their degree distribution, reciprocity and transitivity. Just as each network is associated with multiple individuals, each individual is associated with multiple networks. This is not to licence the rejection of the Coleman diagram, which would amount to throwing the baby with the bath water.




If we dare to suggest a modest modification to the Coleman diagram, it would restore the empirical intuition that hierarchical structures of one-to-many relationships are not as common as network structures of many-to-many. This involves a sense of symmetry between individuals and any other entities one might think about (see figure~\ref{ImgColemanButterfly}). 

\figuremacroW{ImgColemanButterfly}{The Coleman butterfly}{Attempting to account for a symmetry between the individual and the group}{.60}

In this figure, individuals and other entities are each a product of many different elements. When they interact, only a subset of their properties come play a role in the interaction, and might change as a consequence, possibly resulting in lasting cumulative effects that can carry on to other situations. Recall the example of Romeo and Juliet from section~\ref{sec:colemansboat}. They are both affiliated with rival families, but they are also affiliated with the young, those who are prone to fall in love. Each of them is a `macro' product of multiple networks, but in the context of a Capulet's masquerade ball, certain dimensions become more salient and others fade into the background, allowing for the tragic story to unfold. Consider another example, namely the notion of faultlines in groups \citep{lau1998}. Group faultlines are lines that may split a group into subgroups based on the different affiliations of each individual. For example, a group could divide into subgroups based on age, sex or personal values. Thus different tasks or contexts could increase the potential for friction and subgrouping along one of the many possible faultlines. Talk about affirmative-action may generate racial tension, retirement or pension issues may activate faultlines based on age, and a discussion about a perceived glass-ceiling in the organization may activate sex-related divisions, etc. Moreover, in some groups faultlines can align, for example when a group includes five young, white male interns and five senior black females, the group's faultline becomes `stronger,' since many topics can bring to a confrontation, dividing the group along the same lines.

The theoretical consequences of this proposal must be thought through more carefully, but I think it retains the most important element of Coleman's diagram and the essence of micro-foundations, namely the rejection of Durkheimian style, macro-to-macro transitions that do not involve transactions or interactions. This proposed extension does not amount to the adoption of holism. But it does introduce the possibility of a symmetry between entities, placing them all on the same plane and replacing the one-to-many relationship that is typical to micro-foundations with a many-to-many one that, I think, is a closer approximation to the empirical world. 



\section{The Rebirth of Social Physics}


\begin{quotes}
'It is generally in these ill demarcated domains, that the urgent problem lies'\\
\attrib{{Marcel Mauss} \citeyearpar{mauss1973}   }
\end{quotes}


\begin{quotes}
No one descends with such fury and in so great a number as a pack of hungry physicists, adrenalized by the scent of a new problem. \\
\attrib{{Duncan Watts} \citeyearpar[p 62]{watts2004a}   }

\end{quotes}

\begin{quotes}
The idea that science and philosophy are different disciplines meant to complement each other \ldots arouses the desire and also imposes on us the duty to proceed to a confrontation. \\
\attrib{{Henry Bergson} \citep[in the context of a debate with Albert Einstein, quoted in][p 183]{canales2010}   }
\end{quotes}


\noindent The dissertation demonstrated some of the mechanisms that are involved in the co-evolution between micro-level email transactions and meso- and macro- level ties and networks, broadly defined. This concluding chapter began with a reply to a common concern, about the possibility to infer network level constructs from transaction level data.  

The reply depends on the way one wishes to define the social tie, and its relation to social transactions. If one wishes to define the tie in terms of the transactions (in the tradition of Tarde, Homans and others,) there is no problem and no need for further data. If the tie is contingent on the transactions, we can treat it as a latent variable and identify some of its properties through its interaction with the manifest variables of email transactions.

After addressing this concern the findings were presented, organized according to the different mechanisms in the Coleman diagram. The most interesting findings in Chapter 4 are associated with the aggregation link from micro-to-macro on the diagram, and they involved the process by which email based interactions at the micro-level give rise to network patterns at the macro level. The most interesting findings in Chapter 5 are associated with the (macro- and meso-) conditions for action. The model was designed to disentangle between micro-level conditions (the incoming email and its properties) and macro-level ones (general etiquette for email communication, sender/recipient's role in the organization etc.) The third section reviewed the contributions critically, demonstrating some of the empirical and conceptual elements that distinguish between network models based on email mediated transactions and social models based on surveys and questionnaires. This was followed by a section discussing some of the methodological contributions and some general remarks about the theoretical framework of micro-foundations, the way the framework facilitates thinking about and communicating the empirical investigation and some of the puzzles it raises.

%\begin{wrapfigure}{r}{0.35\textwidth}
%  \vspace{-50pt}
%  \begin{center}
%    \includegraphics[width=0.34\textwidth]{ImgStarlingSwarm}
%  \end{center}
%  \vspace{-10pt}
%  \caption[A Swarm of Starlings against a grey sky]{\textbf{A Swarm of Starlings against a grey sky} - shifting and shaping as one, with no apparant leader, what is the mechanism that coordinates their individual actions? \newline\textit{ Photograph by Manuel \citet{presti2007}}}
%  \vspace{-20pt}
%\end{wrapfigure} 

As the academic and systematic study of digitially mediated transactions is entering its second decade \citep{lazer2009}, it is worth thinking of its consequences, in the context of social network studies.  

\begin{wrapfigure}{r}{0.5\textwidth}
  \vspace{-30pt}
  \begin{center}
    \includegraphics[width=0.49\textwidth]{ImgSocialPhysics}
  \end{center}
  \vspace{-10pt}
  \caption[The Cover of Auguste Comte's book 'Social Physics']{\textbf{The Cover of Auguste Comte's book 'Social Physics'} - `A book for the times - to exterminate political vermin and moral quacks'}
  \vspace{-0pt}
\end{wrapfigure} 


Granted, digitally mediated transaction datasets have triggered a heated controversy among social scientists, particularly among those who specialize in the field of social networks. For one thing, the large datasets attracted physicists and mathematicians who are now publishing surprisingly influential papers \citep{lazer2009a}, surprising given that some of them are rightly accused of claiming ownership on discoveries that were already known for decades \citep{scott2011,freeman2011}. Others maintain that traditional network scholars are reluctant to adopt digitally mediated transaction datasets for substantive research because of the data's `theoretical and empirical ambiguity,' and because it is unclear how these datasets stand in relation to traditional network data \citep{quintane2011}.

%Some scholars maintain that the advent of new types of datasets is an opportunity to raise these issues, though these questions have been addressed since the time of Gabriel Tarde \citep{latour2012}. 


But there is another, slightly more optimistic view regarding these new developments. \citet*{latour2012} suggest that we may be witnessing a gestalt switch (in the Kuhnian sense) in the field, a shift from a Durkheimian paradigm back to a Tardian one. According to these authors, the Durkheimian strategy organizes the world into layers of analysis, each two layers linked in a one-to-many relationship. Whether the macro-micro link is contingent or definitional, system effects such as Condorcet's paradox and the prisoner's dilemma (see section \ref{sec:Chp6Distinctive}) give the sense that macro- and micro-level entities are situated on different ontological plains, entities that are different in kind. On the other hand, the Tardian perspective, according to \citet{latour2012}, is a departure from this hierarchical view, in that it adopts a symmetric approach, bringing all entities, both individuals and `social facts' onto one ontological plane, each type of entity  associated with others in a many-to-many relationship, each changing by interacting with the others.  It is too soon to tell whether this rather vague prognosis will be realized, but I think that it would be rather exciting if new types of data challenge us to consider more carefully the properties of transactions and their consequences, before aggregating them into networks. 

This research was a quest for mechanisms that link immediate social actions with the structural properties of networks. It is inspired by a non-Durkheimian  approach, one that replaces the `oversocialized man' \citep{wrong1961}, with a sensitivity to momentary decisions, fleeting events and impulsive (trans)actions. It is driven by the notion that the question `to reply or not to reply' is of greater consequence than the question `to be or not to be.' Many great men and women accompanied us along this journey, reminding us that the controversies are far from contemporary and most probably far from over:\footnote{These names are just a small and non-representative sample, far from exhaustive.} Is the macro-micro link definitional (Homans, Weber, \citet{monge2003}, Margaret Thatcher and the reductionists) or contingent (Simmel,  Mauss, Coleman, L\'evi-Strauss and the structuralists)? Are macro-level entities and micro-level ones different in kind (Durkheim, Nietzsche, structuralists and those studying  system effects) or not (Gabriel Tarde, Bruno Latour)? What is the nature of social action (Simmel, Parsons, Mauss, Weber, Coleman)? Is the individual really a micro entity (Romeo, Juliet and the Coen brothers)? 

Another common thread throughout this work is the way  social ties interact with  transactions, acts of communication and exchanges, meetings and social events. This issue is crucial to those who construct models of social networks from digitally mediated transaction datasets. It also problematizes the role of the technological artefact that mediates communication transactions, for its properties shape the way transactions and network structures interact. Surprisingly perhaps, even this question of action and ties is not limited to our time. The dissertation opened with a poem describing the process of tie formation, beginning with innocent and playful acts of courtship, climbing the hysteresis curve with passion and swept away by a storm of emotion. The same process, only in reverse, is described by Virginia Wolf almost a century ago. Following a rather dull social gathering, the acquaintances of lady Bruton part, each going their own way, and as the memory of the event fades, the emotions associated with the social ties dissipate in a manner not unlike the one described in figure~\ref{ImgTimeDependentTieWeightFunction}. In contrast to the process of tie formation, here there is neither joy nor anguish, neither benefits nor costs, neither animal spirits nor social facts, but only the dwindling of spirit, the drifting away in silence, a sense of lethargy, resignation and indifference. 

\begin{quotes}
And Lady Bruton went ponderously, majestically, up to her room, lay, one arm extended, on the sofa. She sighed, she snored \ldots And they went further and further from her, being attached to her by a thin thread (since they had lunched with her) which would stretch and stretch, get thinner and thinner as they walked across London; as if one's friends were attached to one's body, after lunching with them, by a thin thread, which (as she dozed there) became hazy with the sounds of bells striking the hour or ringing to service, as a single spider's thread is blotted with rain-drops, and, burdened, sags down. So she slept [\ldots] lying on the sofa, let the thread snap; snored.\\
\attrib{Mrs. Dalloway, \citep{woolf2012}   }
\end{quotes}



%Charlie hands him his parcel.
%. . . Keep this for me, till I get back.
%Barton, snuffling, accepts the package.
%. . . It's just personal stuff. I don't wanna drag it with me, but I don't trust  'em downstairs, and I'd like to think it's in good hands.

%Still snuffling:
%BARTON
%Sure, Charlie.
%CHARLIE
%Funny, huh, when everything that's important to a guy, everything he wants to keep from a lifetime - when he can fit it into a little box like that. I guess . . . I guess it's kind of pathetic.

% Ideas of Carsten: the point you make here is that SNA has wrong assumptions by not taking into account the digital medium. The medium matters, detail plays a role in how things play out in the macro scale. And increasing diversity means thwta we need to understand how it works. 

% Possible RQ: 
% 1. The role of technology mediation in the 
% 2. The co-evolution of transactions and network. 
% 3. 

% Peter Abell: So - what is your view? difference in kind or differnce in order?
% TODO - change 'definitional' to 'constitutive'. 



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